Multivariate regression with measurement error: bias analysis and estimation
Why this work is in the frame
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Bibliographic record
Abstract
Multivariate regression models are commonly used to examine associations in multivariate data, and various methods have been proposed to characterise distinct features of such data across different settings. The validity of those methods, however, is compromised by the presence of measurement error. Despite extensive research on measurement error in univariate data, the impact of measurement error on the analysis of multivariate data remains an interesting topic to explore. This paper rigorously examines the measurement error effects on multivariate regression models and quantifies the asymptotic bias and covariance matrix for the naïve method that ignores measurement error. We further develop three estimation methods to correct the measurement error effects under different scenarios, including the case with instrument variables. The asymptotic properties of these methods are established accordingly. Lastly, extensions that apply nonparametric techniques to investigate the relationship between responses and covariates contaminated by measurement error are discussed.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.014 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it